On the Ricci flow and emergent quantum mechanics

被引：7
|
作者：
Isidro, Jose M. [1 ]
Santander, J. L. G. [1 ]
Fernandez de Cordoba, P. [1 ]
机构：
[1] Univ Politecn Valencia, Inst Matemat Pura & Aplicada, Grp Modelizac Interdisciplinar, Valencia 46022, Spain
来源：
FOURTH INTERNATIONAL WORKSHOP DICE 2008: FROM QUANTUM MECHANICS THROUGH COMPLEXITY TO SPACETIME: THE ROLE OF EMERGENT DYNAMICAL STRUCTURES | 2009年 / 174卷
关键词：
TENSOR;
D O I：
10.1088/1742-6596/174/1/012033
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential function that is proportional to the Ricci scalar curvature of configuration space. This allows one to obtain Schrodinger quantum mechanics from Perelman's action functional: the quantum-mechanical wavefunction is the exponential of i times the conformal factor of the metric on configuration space. We explore links with the recently discussed emergent quantum mechanics.
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页数：7
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